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Mazón, J.M.; Rossi, J.D.; Toledo, J. "Fractional p-Laplacian evolution equations" (2016) Journal des Mathematiques Pures et Appliquees. 105(6):810-844
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Abstract:

In this paper we study the fractional p-Laplacian evolution equation given by. ut(t,x)=∫A1/|x-y|N+sp|u(t,y)-u(t,x)|p-2(u(t,y)-u(t,x))dy for x∈Ω, t>0, 0 < s< 1, p≥ 1. In a bounded domain Ω we deal with the Dirichlet problem by taking A = RN and u= 0 in RN\\Ω, and the Neumann problem by taking A=. Ω. We include here the limit case p= 1 that has the extra difficulty of giving a meaning to u(y)-u(x)|u(y)-u(x)| when u( y) = u( x). We also consider the Cauchy problem in the whole RN by taking A=Ω=RN. We find existence and uniqueness of strong solutions for each of the above mentioned problems. We also study the asymptotic behaviour of these solutions as t→∞. Finally, we recover the local p-Laplacian evolution equation with Dirichlet or Neumann boundary conditions, and for the Cauchy problem, by taking the limit as s→1 in the nonlocal problems multiplied by a suitable scaling constant. © 2016 Elsevier Masson SAS.

Registro:

Documento: Artículo
Título:Fractional p-Laplacian evolution equations
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain
CONICET and Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina
Departament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain
Palabras clave:Cauchy problem; Dirichlet problem; Fractional Sobolev spaces; Neumann problem; P-Laplacian
Año:2016
Volumen:105
Número:6
Página de inicio:810
Página de fin:844
DOI: http://dx.doi.org/10.1016/j.matpur.2016.02.004
Título revista:Journal des Mathematiques Pures et Appliquees
Título revista abreviado:J. Math. Pures Appl.
ISSN:00217824
CODEN:JMPAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v105_n6_p810_Mazon

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Citas:

---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2016) . Fractional p-Laplacian evolution equations. Journal des Mathematiques Pures et Appliquees, 105(6), 810-844.
http://dx.doi.org/10.1016/j.matpur.2016.02.004
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Fractional p-Laplacian evolution equations" . Journal des Mathematiques Pures et Appliquees 105, no. 6 (2016) : 810-844.
http://dx.doi.org/10.1016/j.matpur.2016.02.004
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Fractional p-Laplacian evolution equations" . Journal des Mathematiques Pures et Appliquees, vol. 105, no. 6, 2016, pp. 810-844.
http://dx.doi.org/10.1016/j.matpur.2016.02.004
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. Fractional p-Laplacian evolution equations. J. Math. Pures Appl. 2016;105(6):810-844.
http://dx.doi.org/10.1016/j.matpur.2016.02.004